Statement Sums Involving Exponent and Power


 
 
Concept Explanation
 

Statement Sums Involving Exponent and Power

To solve statement sums involving exponents and powers. First, frame the equation using the given values in the questions and then solve using BODMAS ( Bracket, Of, Division, Multiplication, Addition and Subtraction)

Illustration 1: By what number should left (frac{-3}{2}right )^-^3 be divided so that the quotient is left(frac{9}{4}right)^-^2?

Solution: Let the number by which we should divide left (frac{-3}{2}right )^-^3 be x . So, we have

frac{left(frac{-3}{2}right)^-^3}{x}=left (frac{9}{4}right)^-^2

After cross multiplication, we have

left(frac{-2}{3}right)^3 =left(frac{4}{9}right)^2;;times;;x                                        left [ because a^{-m}=frac{1}{a^{m}} right ] ;and; left [left ( frac{a}{b} right )^{-1}=frac{b}{a} right ]

frac{-8}{27} =frac{16}{81};;times;;x

x = frac{-8}{27}timesfrac{81}{16}

x=frac{-3}{2}

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Sample Questions
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Question : 1

Evaluate:  large dpi{100} Rightarrow 3^{frac{1}{3}} times 6^{^{frac{2}{3}}} times 4^{frac{1}{3}}

Right Option : B
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Explanation
Question : 2

 Express 392 as a product of powers of their prime factors:

Right Option : C
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Explanation
Question : 3

By what number should (-12)^{-1} be divided so that the quotient may be left ( frac{2}{3} right )^{-1}.

Right Option : C
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Explanation
 
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